Direct Z-scheme GaN/WSe2 heterostructure for enhanced photocatalytic water splitting under visible spectrum

van der Waals heterostructures are widely used in the field of photocatalysis due to the fact that their properties can be regulated via an external electric field, strain engineering, interface rotation, alloying, doping, etc. to promote the capacity of discrete photogenerated carriers. Herein, we fabricated an innovative heterostructure by piling monolayer GaN on isolated WSe2. Subsequently, a first principles calculation based on density functional theory was performed to verify the two-dimensional GaN/WSe2 heterostructure and explore its interface stability, electronic property, carrier mobility and photocatalytic performance. The results demonstrated that the GaN/WSe2 heterostructure has a direct Z-type band arrangement and possesses a bandgap of 1.66 eV. The built-in electric field is caused by the transfer of positive charge between the WSe2 layers to the GaN layer, directly leading to the segregation of photogenerated electron–hole pairs. The GaN/WSe2 heterostructure has high carrier mobility, which is conducive to the transmission of photogenerated carriers. Furthermore, the Gibbs free energy changes to a negative value and declines continuously during the water splitting reaction into oxygen without supplementary overpotential in a neural environment, satisfying the thermodynamic demands of water splitting. These findings verify the enhanced photocatalytic water splitting under visible light and can be used as the theoretical basis for the practical application of GaN/WSe2 heterostructures.


Introduction
Hydrogen energy is anticipated to be an alternative fuel to fossil fuels in the near future, [1][2][3] and in this case, photocatalytic water splitting is an attractive approach to produce hydrogen. 4 The traditional photocatalytic material TiO 2 has a wide band gap (BG) of 3.20 eV, which is only activated by ultraviolet light with a wavelength of less than 385 nm and its hydrogen production efficiency is extremely low. 5 Alternatively, two-dimensional (2D) transition metal dichalcogenides (TMDCs) such as WSe 2 , MoS 2 , and MoSe 2 have signicant application prospects in photocatalytic water splitting due to their excellent electronic properties, high carrier mobilities and visible-light response. In particular, it has been conrmed theoretically that monolayer WSe 2 has robust photoluminescence and high carrier mobility (705 cm 2 V −1 s −1 ), which are superior to that of MoS 2 and MoSe 2 . [6][7][8] Nevertheless, the photocatalytic performance of monolayer WSe 2 is still limited owing to its high transmittance and poor photogenerated electron-hole separation efficiency. Hence, the use of a co-catalyst to reduce the electron-hole recombination is strongly recommended.
In recent years, some studies have proven that the construction of van der Waals heterostructures (vdWHs) is a valid approach to improve the photocatalytic efficiency of 2D materials. 9,10 vdWHs retain the electronic properties of individual layers and the interface effect of heterostructures endow them with some properties that are not present in their respective components, such as regulating the bandgap energy and improving the segregation efficiency of photogenic electron-hole pairs. 11,12 Traditional type II heterostructures have the advantages of response in an expanded spectrum range and promoted carrier separation, 13 but their redox ability is poor. Thus, the design and fabrication of novel direct Z-scheme photocatalysts are attracting increasing interest to improve the redox ability and transfer performance of photo-generated charges. [14][15][16] GaN monolayers are very promising for application in highperformance opto-electronic devices due to their semiconducting character with a suitable bandgap of about 2.3 eV, 17,18 which is narrower than that of bulk GaN. 19 Previous research disclosed that GaN shares an identical hexagonal conguration and related lattice constants with TMDCs, making them compatible. 20 Also, a GaN thin lm was prepared via chemical vapor deposition from SL-WSe 2 /c-sapphire to achieve GaN/WSe 2 heterostructures. 21 R. Meng et al. revealed that the existence of band offsets and intrinsic electric elds leads to reinforced photocatalytic activity between WSe 2 /GaN and WS 2 /GaN. 22 Shaoqian Yin et al. studied the effects of modifying the electric eld and strain on the optical and electronic characteristics of GaN/WSe 2 heterostructures with various stacking congurations. However, a systematic study has not been performed to date on the photocatalytic performance of GaN/WSe 2 heterostructures. 23 In this study, the structural stability, electronic properties, carrier mobilities, and photocatalytic performance of GaN/WSe 2 heterostructures were explored via rst-principles calculations. The calculations of the energy band gap presented that the GaN/ WSe 2 heterostructure is a representative direct Z-scheme with a built-in electric eld from GaN to WSe 2 . Meantime, the carrier mobilities of the GaN/WSe 2 heterostructure, which inuence the dissociation efficiency, was also amplied. In addition, the calculation of the Gibbs free energy of the GaN/WSe 2 system clarify the oxygen evolution reaction (OER) process. Consequently, it was inferred that GaN/WSe 2 heterostructures, which possess superior photocatalytic capacities under visible light, are favorable photocatalysts in the eld water splitting.

Calculation methods and models
The theoretical analyses were manipulated entirely through the Vienna ab initio simulation package (VASP) 24 within the projector augmented plane-wave (PAW) pseudopotentials using density functional theory (DFT). The Perdew-Burke-Ernzerhof (PBE) algorithm was adopted to conrm the exchangecorrelation functional. 25 Two-dispersion correction of DFT-TS 26 and DFT-D3 (ref. 27) was considered in the computation for clarifying the impacts of non-covalent forces. The valence electron schemes were as follows: 3d 10 4s 2 4p 1 for Ga, 2s 2 2p 3 for N, 5d 4 6s 2 for W, and 4s 2 4p 4 for Se. A Monkhorst Pack k-point grid of 7 × 7 × 1 and a cutoff energy of 480 eV were employed in the rst Brillouin zone. The maximum force was set as 0.01 eV Å −1 and the energy convergence threshold was 10 −5 eV.

Interface stability
To inspect the impact of the interfacial interactions between the GaN and WSe 2 nanosheets on the structural stability of GaN/ WSe 2 combinations, the compositional dependence of the total energy is discussed. Six representative parallel alignments of GaN/WSe 2 heterostructures are displayed in Fig. 1. To calculate the structural stability of the six stacked models quantitatively, the D3 and TS dispersion corrections were included to calculate the relative total energies of the six patterns (compared with the steadiest model) applying the PBE method, respectively, as shown in Fig. 2. The results show that the different calculation methods have analogous variation tendencies in the related total energies of the six congurations, demonstrating that the computational outcomes are dependable. Also, the gure shows that model V has the lowest relative energy among the models with the DFT-D3 algorithm, while model VI has the lowest relative energy compared with the others with DFT-TS algorithm. Hence, all sequent calculations were built on these two models.
To further study the structural stability of the GaN/WSe 2 heterostructure, the lattice mismatch ratio and mismatch energy between the two monolayers were calculated. The lattice mismatch ratio is described as R mis =(a 2 − a 1 )/a 1 , where a 1 and a 2 represent the lattice constants of the GaN and WSe 2 monolayers, respectively. Table 1 lists the R mis of the GaN/WSe 2 heterostructures calculated by the DFT-D3 and DFT-TS methods, which are 3.00% and 3.92%, respectively, showing a perfect match. 31 Moreover, the lattice mismatch energies of the GaN/ WSe 2 heterostructures were determined using the following equation: where E (GaN)a and E (WSe 2 )a are the overall energies of isolated GaN and WSe 2 under the equilibrium lattice parameters of the GaN/WSe 2 heterostructures, respectively. E GaN and E WSe 2 indicate the whole energies of the single GaN and WSe 2 nanosheets before contact. S represents the interfacial area of the Table 1 Calculated lattice parameters (Å), lattice mismatch ratio (%), cohesive energies (meV Å −2 ), mismatch energies (meV Å −2 ), vdW binding energies (meV Å −2 ) and equilibrium interlayer distances (Å) of GaN/WSe 2 heterostructures using the dispersion-correction DFT-TS and DFT-D3 approaches after geometric relaxation

Model Method
GaN heterostructure. The mismatch energy results are exhibited in Table 1. DE mis computed by DFT-D3 and DFT-TS approaches is 1.84 meV Å −2 and 4.14 meV Å −2 , respectively, which is substantially below that of WS 2 /WSe 2 , 34 MoS 2 /WSe 2 , 33 and graphene/WSe 2 . 32 In the heterostructure, the lattice mismatch of the isolated GaN and WSe 2 caused by strain-driven interactions is almost negligible.
To elucidate the adsorption interaction between the GaN and WSe 2 monolayers, the two above-mentioned methods were chosen to attain the interfacial cohesive energy, E coh , at different interlayer distances, d. E coh is expressed as follows: where E GaN/WSe 2 , E GaN , and E WSe 2 correspond to the whole energies of relaxed GaN/WSe 2 heterostructure, GaN monolayer and WSe 2 monolayer, separately. The E coh of the GaN/WSe 2 composites at the most stable interlayer spacing is −0.78 meV Å −2 and −2.55 meV Å −2 for DFT-D3 and DFT-TS, respectively, as displayed in Table 1. It is noticeable that the negative E coh values imply stable heterostructures. 35,36 Therefore, the cohesion between GaN and WSe 2 stabilizes the geometry. In addition, the E coh trends calculated using the two methods are very similar to the changes in the interfacial space, proving the dependability of the calculated results. Finally, the van der Waals energy was introduced to quantitatively describe the magnitude of the interlayer van der Waals force, which is dened as and its magnitude is determined by the lattice mismatch energy and the interface binding energy. The calculation formula is as follows: The calculated results are 2.61 eV and 6.69 eV, which are within the normal vdW binding energy range, 37,38 indicating the existence of slight van der Waals forces in the GaN/WSe 2 heterostructures.
In the case of the GaN/WSe 2 heterostructure, the equilibrium interfacial space between GaN and WSe 2 is 3.09 Å with DET-D3 and 3.32 Å with DFT-TS, respectively, which is the canonical distance of vdW force. 39 Besides, given that R mis under DET-D3 is smaller than that with DET-TS, the subsequent calculations are based on model V of the GaN/WSe 2 heterostructure with the DET-D3 method. The results of model VI of the GaN/WSe 2 heterostructure with the DET-TS method are demonstrated in the ESI. †

Electronic property
The band arrangements of the GaN monolayer, WSe 2 monolayer and GaN/WSe 2 composites were investigated using the PBE functional module. The Fermi level of the three systems was set as the level zero energy, and the high symmetry sites G (0,0,0), M (0,0.5,0) and K (−0.333,0.667,0) in the Brillouin zone were used as observation routes to study the band alignment of the system with the range limited from −4 eV to 5 eV. Fig. 3(a) shows that monolayer GaN is a semiconductor with an indirect BG of 2.13 eV, where the valence band maximum (VBM) is settled at the K point, while the conduction band minimum (CBM) is settled at the G point. This is theoretically in accordance with the established research. 40 The VBM and CBM of the single-layer  WSe 2 were both set near the K point, which denotes that WSe 2 is a semiconductor with a direct BG of 1.65 eV. The calculated results of WSe 2 are similar to that reported by R. S. Meng, 41 as demonstrated in Fig. 3(b). Fig. 3(c) presents the band diagram of the GaN/WSe 2 heterostructure. Both the VBM and CBM are located at the high symmetry point K, and thus it is a direct semiconductor with a BG of 1.47 eV. Compared with the indirect BG semiconductor, the direct bandgap semiconductor has a higher absorption coefficient for photo-generated electron-hole pairs and higher light utilization rate, and thus it is more suitable for photocatalysis. 42 The forbidden bandwidth of the GaN/WSe 2 heterostructure is 1.47 eV, which is slightly lower than that of the GaN and WSe 2 monolayers, and its energy levels are denser. This is conducive to the migration of electrons, thereby improving the photocatalytic activity. Also, the BG of the GaN/WSe 2 heterostructure is larger than that required for photocatalytic water splitting, which is 1.23 eV. In addition, comparing the three images in Fig. 3(a-c), it can be found that the energy band structure of the GaN/WSe 2 heterostructure is similar to the energy band alignments of the two monolayers, and almost retains that of GaN and WSe 2 to a large extent. Therefore, it can be speculated that the binding force between the heterostructure layers is weak van der Waals force, and the interaction force when the two monolayers are combined is small, which also corresponds with the above-mentioned result.
The density of states (DOS) usually reects the distribution of electrons in each system. To further elucidate the electronic structure of the GaN/WSe 2 heterostructure, we also calculated the density of states of the GaN/WSe 2 heterostructure, GaN monolayer and WSe 2 monolayer. The density curve range was −2 eV to 3 eV for analysis, as illustrated in Fig. 3(e and f). The VBM of monolayer GaN consists mainly of Ga-4p and N-2p states, whereas the CBM consists of N-2p states, are displayed in Fig. 3(e). The VBM and CBM of monolayer WSe 2 consist primarily of W-5d and Se-4p states, as presented in Fig. 3(f). Apparently, the VBM is derived from GaN (orange shaded region in Fig. 3(e)), while the CBM of the GaN/WSe 2 heterostructure originates from WSe 2 (blue shaded region in Fig. 3(f)). The overlap may be caused by orbital hybridization, and the occurrence of orbital overlap will result in a reduction in the BG, which is more advantageous to improve the catalytic performance of the photocatalytic material. 43 It is well-known that the valence band offset (VBO) and the conduction band offset (CBO) are at the related sites of the VBM and the CBM of two sides of the interfacial space, respectively, which can considerably modify the charge transfer capacity of the heterostructures under illumination. 44 In addition, VBO, CBO, and BG can be dened as CBM , and E g = EWSe 2 CBM − EGaN VBM, respectively. Under the equiponderant interfacial condition, the correlation of VBO, CBO, the BG values is VBO (0.12 eV) < CBO (0.65 eV) < BG (1.47 eV). Accordingly, it can be reliably inferred that the GaN/WSe 2 heterostructure shows a type-II or Z-scheme band structure, which is consistent with the conclusion of band alignment, leading to the spatial segregation of the photogenerated carrier pairs. 45 The charge transfer phenomenon at the heterostructure interface can be illuminated by calculating the interfacial work function of the GaN monolayer, WSe 2 monolayer and GaN/WSe 2 heterostructures. 46 The calculation formula is as follows: where E vac and E F express the vacuum energy level and the Fermi energy level, respectively, and the vacuum energy level is taken as 4.5 eV. The GaN/WSe 2 heterostructure curve is the sum of the GaN monolayer and WSe 2 monolayer. The surface work functions of the GaN monolayer (Fig. 4), WSe 2 monolayer and GaN/WSe 2 heterostructure are 4.340 eV, 5.125 eV and 4.954 eV, respectively, and the work function of the heterostructure lies between that of isolated GaN and WSe 2 . and the electrons usually ow from the low side of the work function to the high side. Therefore, when the WSe 2 and GaN monolayers are in contact, electrons aggregate at the interface of the WSe 2 side to form a negative region, and the holes accumulate at the GaN side to form a positive region, thereby forming a built-in electric eld pointing from the GaN layer to the WSe 2 monolayer. Given that the Fermi levels of the two monolayers are different, the energy bands shi accordingly until the Fermi levels of the two monolayers reach equilibrium. The presence of a built-in electric eld can improve the mobility of carriers, thereby enhancing the dissociated efficiency of photo-induced electronhole pairs, reducing the recombination probability of carriers, and improving the photocatalytic properties of the heterostructure. The position of the band edge of a semiconductor is very important for evaluating its redox ability and photocatalytic performance. It is apparent that with the emergence of heterostructures, the E F of two pristine materials will achieve equilibrium. Consequently, the isolated GaN intimately contacts with WSe 2 , which will provoke a negative shi of 0.614 V in E F for GaN and induce a positive shi of 0.171 V for the WSe 2 nanoslab. Due to the migration of electrons from monolayer GaN to WSe 2 with abandoned holes in the GaN nanolayer, the edge potentials in the CB and VB of GaN are −0.73 V and 1.40 V at the GaN/WSe 2 heterostructure aer equalizing, singly. Meanwhile, that of the WSe 2 slab is 0.02 V and 1.67 V, respectively. It can be deduced that the VB edge potential of WSe 2 is 0.27 V lower than that of monolayer GaN; meantime, the CB edge of GaN is 0.75 V larger than that of the WSe 2 slab. As shown in Fig. 5, the photogenerated carriers obey two different routes, as follows: (1) electron transformation: on the one hand, the photogenerated electrons transfer from the VB to the CB under illumination. On the other hand, the built-in electric eld of the interface prevents electrons from migrating from the isolated GaN to WSe 2 . Meanwhile, the occurrence of CBO impedes electrons implanting in the CB of the monolayer WSe 2 , and the photoinduced holes in the VB of the single WSe 2 hinder their transitions to the VB of the GaN nanosheet. (2) Recombination of charges: in the CB of isolated WSe 2 , the photogenerated electrons will rapidly recombine with the photogenerated holes in the VB of the isolated GaN, by virtue of the close range of charge conveyance between the WSe 2 and GaN layer. Accordingly, photogenerated carriers can excellently detach aer the construction of the heterostructure. Finally, it was determined that the GaN/WSe 2 heterostructure is a representative direct Zscheme semiconductor, which is consistent with the consequences of band alignment and DOS. The type of band arrangement can make electron-hole pairs separate effectively and diminish the recombination of carriers, increase the lifetime of minority carriers, and simultaneously retain the redox ability of the internal carriers, which is further enhanced compared to the traditional type-II heterostructure photocatalytic properties.
The two important potentials for water splitting are the O 2 / H 2 O electrode potential of 1.23 V, which can generate oxygen, and the standard hydrogen electrode H + /H 2 O potential of 0 V. Given that the GaN/WSe 2 heterostructure is a Z-type heterostructure, the potential at the CB position of the heterostructure is −1.06 eV and the VB position is 1.47 eV. Comparing the water splitting potential, it can be known that the energy at the CBM in the GaN/WSe 2 heterostructure is more negative than that of the standard hydrogen electrode (H + /H 2 O), and the VBM is more positive than that of the O 2 /H 2 O electrode. The BG of the GaN/WSe 2 heterostructure is larger than the potential required for water splitting, and thus it can be deduced that the GaN/ WSe 2 heterostructure can be applied for either the hydrogen evolution reaction (HER) or oxygen evolution reaction (OER), making it a good photocatalytic heterostructure.
The formation of a heterostructure will induce interactions between the interfaces, leading to the transfer and redistribution of charges at the interface. This can be studied by calculating the differential charge density of the heterostructure. The plane differential density is dened as Dr, which can be calculated using the following formula: where r GaN/WSe 2 represents the charge density of the entire GaN/ WSe 2 heterostructure system, and r GaN and r WSe 2 represent the charge density of the GaN monolayer and WSe 2 monolayer, respectively. The plane charge differential density curve and three-dimensional charge differential density map in the Z direction of the GaN/WSe 2 heterostructure were obtained, as shown in Fig. 5. For the plane charge differential density curve in Fig. 5, the blue area represents the depletion of charges and the yellow area represents the charge accumulation. Electrons accumulate in the WSe 2 slab and are consumed in the GaN slab, elucidating that electrons migrate from the GaN to WSe 2 nanosheet. To quantitatively articulate the charge density, the Bader charge analysis under equilibrium was executed. The negative charges of 0.016 e per atom shi from the GaN nanosheet to the WSe 2 aer they contact each other. It is generally acknowledged that the variation in the populations is consistent with the conclusions of the charge density difference. Simultaneously, in Fig. 5, it indicates that for the benet of implementing stability, segments of electrons in GaN relocate to WSe 2 in the interface,  which causes a positive charge region in the surface of GaN and negative charge in that of WSe 2 . It can be conrmed that the GaN/WSe 2 heterostructures can take advantage of the built-in electric eld pointing from GaN to WSe 2 to efficiently separate the photogenerated electrons and holes (Fig. 6).

Carrier mobility
Generally, the carrier mobility originates from the deformation potential, which is a pivotal factor to estimate photocatalytic properties and should be calculated systematically. 47 The methods for the calculation of the carrier mobility are elaborated in the ESI. † By utilizing compressive and tensile strains, the in-plane C 2D and E 1 i of the isolated GaN, WSe 2 and GaN/ WSe 2 were assessed by tting the data into parabolic and linear curves, which are exhibited in Fig. 7, S5 and S6 in the ESI, † respectively. Also, Table 2 displays the acquired m*, C 2D , E 1 i and m 2D .
The monolayer GaN and WSe 2 and GaN/WSe 2 heterostructure exhibit different C zig 2D and C arm 2D in the zigzag and armchair directions, which determines that their physical stress responses are totally anisotropic. In addition, the carrier mobilities of the WSe 2 monolayer is lower than that of nanosheet GaN because of its smaller elastic modulus and higher deformation potential. These conclusions are in accordance with previous theoretical and experimental results. [48][49][50][51] Alternatively, the limitations of the deferent rates of photogenerated carriers are mainly owing to the low electron mobilities of the GaN slab and low carrier mobilities of the WSe 2 slab, essentially increasing the recombination of photogenerated electron-hole pairs. Monolayer GaN and WSe 2 detrimentally obstruct the photocatalytic activities, and thus is signicant to fabricate GaN/WSe 2 heterostructures. Consequently, the electron and hole mobilities of the GaN/WSe 2 heterostructure are 4149.37 cm 2 V −1 s −1 and 2101.71 cm 2 V −1 s −1 along the zigzag direction, and 4328.33 cm 2 V −1 s −1 and 2395.94 cm 2 V −1 s −1 along the armchair direction, respectively, indicating that the electrons in the GaN/WSe 2 heterostructure, which have a tendency of spreading and moving along both the zigzag and armchair directions, are superior to holes. Additionally, water oxidation reactions take place in the WSe 2 nanosheet through photogenerated holes, the water reduction reactions emerge in the GaN monolayer, as can be seen in Fig. 5. In comparison to the single layers, the electron mobilities of the GaN/WSe 2 heterostructure in the zigzag pathway achieve a remarkable enhancement, which are 19 times and 21 times that of the isolated GaN and WSe 2 , respectively. Meanwhile, 11 times and 67 times versus monolayer GaN and WSe 2 are achieved along the   armchair pathway. Correspondingly, the hole mobilities of the GaN/WSe 2 heterostructure in the zigzag direction and armchair direction are improved by 4 times and 19 times compared with that of nano-slab WSe 2 , respectively. In short, GaN/WSe 2 heterostructures with noticeable carrier mobilities exhibit tremendous potential for application in the photocatalytic eld.

Photocatalytic performance
To additionally validate if water splitting reactions will initiate spontaneously, the thermodynamic practicability of applying the GaN/WSe 2 heterostructures as photocatalysts was explored. The complete water splitting mechanism of the GaN/WSe 2 heterostructure under light irradiation was divided into the HER and oxygen OER. Herein, the Gibbs free energy (DG) of the water splitting reaction were obtained from the report by Nørskov et al. 52 The method for the calculations of DG is elaborated in the ESI. † Acid (pH = 0) and neutral (pH = 7) conditions were both considered. Universally, the HER tends to occur under a suitable potential than the OER, and thus investigating the thermodynamic driving force for the OER is sufficient. When the OER reaction happens, the structures of the most stable OH*, O*, and OOH* intermediates adsorbed at the WSe 2 interface during the standard four-electron transport reaction paths and the relative variation in DG are elucidated in Fig. 8. The computed DG of OH*, O*, and OOH* in the dark (U h = 0 V) when pH = 0 is 1.74 eV, 2.81 eV and 4.87 eV, respectively. Therefore, the emergence of the OOH* intermediate is the ratedetermining process, and thus the OER process can proceed spontaneously when providing a 1.47 eV external potential afforded by photogenerated holes. It is apparent that the computed DG is enhanced in the initial and third steps, but decreases in the second and fourth reaction when pH = 0 and U h = 1.23 V.
Interestingly, when the external potential realizes 1.67 V with pH = 0, the various trends of DG are the same as the conditions at pH = 0 and U h = 1.23 V. The results indicate that the OER step of water splitting will not spontaneously originate at pH = 0. Until the external potential reaches 1.88 V at pH = 7, the DG of the ultimate processes (DG A , DG B , DG C , and DG D ) shis to negative values, as exhibited in Fig. 8(c) (presented by the green line), which ascertains that the OER process will spontaneously occur at pH = 7 with light illumination. In conclusion, the GaN/ WSe 2 heterostructures can initiate water decomposition without a thermodynamic driving force under irradiation in a neutral environment.

Conclusions
In summary, we comprehensively investigated the electronic, optical and photocatalytic properties of the GaN/WSe 2 heterostructure. Model V manifested a benecial Z-scheme band arrangement with a built-in electric eld pointing from GaN to WSe 2 , while model VI displayed a detrimental type I band alignment. In the case of model V, the electron mobilities of the GaN/WSe 2 heterostructure are signicantly enhanced compared to that of monolayer GaN and WSe 2 , and the hole mobilities enlarge substantially compared to that of isolated WSe 2 . In addition, the CB edge of GaN and VB edge of the WSe 2 monolayer can yield robust reduction and oxidation reaction, respectively. Then, we explored the photocatalytic OER on the heterostructure and found that the reaction spontaneously proceeded in a neutral environment. These ndings provide a theoretical basis for the practical application of 2D GaN/WSe 2 heterostructures and provide insight for subsequent research on van der Waals heterostructures.

Conflicts of interest
The authors declare no competing nancial interest.